The magnetic white dwarf SDSS J121209.31+013627.7 exhibits a weak , narrow H \alpha emission line whose radial velocity and strength are modulated on a period of \sim 90 minutes . Though indicative of irradiation on a nearby companion , no cool continuum component is evident in the optical spectrum , and IR photometry limits the absolute magnitude of the companion to M _ { J } > 13.37 . This is equivalent to an isolated L5 dwarf , with T _ { eff } < 1700 K. Consideration of possible evolutionary histories suggests that , until \sim 0.6 Gyr ago , the brown dwarf orbited a \sim 1.5 M _ { \sun } main seqeunce star with P \sim 1 yr , a \sim 1 AU , thus resembling many of the gaseous superplanets being found in extrasolar planet searches . Common envelope evolution when the massive star left the main sequence reduced the period to only a few hours , and ensuing angular momentum loss has further degraded the orbit . The binary is ripe for additional observations aimed at better studying brown dwarfs and the effects of irradiation on their structure .